MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
crazy guy Grade: Upto college level
        


1.      If f(x) is a monotonically increasing function " x Î R, f "(x) > 0 and f -1(x) exists, then prove that å{f -1(xi)/3} < f -1({x1+x2+x3}/3), i=1,2,3


 


2.      Discuss the applicability of Rolle’s theorem to f(x)=log[x2+ab/{(a+b)x}] in the interval [a,b].


 


3.       y = f(x) be a curve passing through (1,1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Form the differential equation and determine all such possible curves.


 


4.        Let f be a real-valued function defined for all real nos. x such that, for some positive constant a, the equation f(x+a) = 1/2 + Ö(f(x)-(f(x))2) holds for all x. (a) Prove that the function f is periodic. (b) For a=1, give an example of a non-constant function with the required properties.



  1. Sum the series: 1 + 4x + 9x2 + ...

  2. If w is a root of x4=1 then Show that a + bw + cw2 + dw3 is a factor of






























a



b



c



d



b



c



d



a



c



d



a



b



d



a



b



c



     


                                                                                                                                                       


 


 


Hence Show that the det is equal to -(a+b+c+d)(a-b+c-d){(a-c)2+(b-d)2}.



  1. Prove that if a > 0, b > 0 then for any x and y the following inequality holds true: a.2x+b.3y+1 £ Ö(4x+9y+1)Ö(a2+b2+1)

  2. Given 6 numbers which satisfy the relations:
    y2 + yz + z2 = a2
    z2 + zx + x2 = b2
    x2 + xy + y2 = c2
    Determine the sum x+y+z in terms of a, b, c. Give geometrical interpretation if the numbers are all positive.

  3. When 03) + x2/(1-x3)(1-x5) + x4/(1-x5)(1-x7) + ....


10.   Find all real p, q, a, b such that we have (2x-1)20 - (ax+b)20 = (x2+px+q)10 for allx.


 


11.  f(x+y) = f(x) + f(y) + 2xy - 1 " x,y. f is differentiable and f ‘(0) = cos a. Prove that f(x) > 0 " x Î R. 


7 years ago

Answers : (1)

Vijay Luxmi Askiitiansexpert
357 Points
										

Please ask your question one by one ...one question in one post ...

7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete AIPMT/AIIMS Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details